During the breakfast with my colleagues, a question popped into my head:

What is the fastest method to cool a cup of coffee, if your only available instrument is a spoon?

A qualitative answer would be nice, but if we could find a mathematical model or even better make the experiment (we don't have the means here :-s) for this it would be great! :-D

So far, the options that we have considered are (any other creative methods are also welcome):

Stir the coffee with the spoon

Pros:

The whirlpool has greater surface than the flat coffee, so it is better for heat exchange with the air.

Due to the difference of speed between the liquid and the surrounding air, the Bernoulli effect should lower the pressure and that would cool it too to keep the atmospheric pressure constant.

Cons:

Joule effect should heat the coffee.

Leave the spoon inside the cup

As the metal is a good heat conductor (and we are not talking about a wooden spoon!), and there is some part inside the liquid and other outside, it should help with the heat transfer, right?

A side question about this is what is better, to put it like normal or reversed, with the handle inside the cup? (I think it is better reversed, as there is more surface in contact with the air, as in the CPU heat sinks).

Insert and remove the spoon repeatedly

The reasoning about this is that the spoon cools off faster when it's outside.

(I personally think it doesn't pay off the difference between keeping it always inside, as as it gets cooler, the lesser the temperature gradient and the worse for the heat transfer).

20 Answers
20

There were four trials, each lasting 10 minutes. Boiling water was poured into the canning jar, and the spoon was taken from the ice bath and placed into the jar. A temperature reading was taken once a minute. After each trial the water was poured back into the boiling pot and the spoon was placed back into the ice bath.

Congratulations on having one of the highest scoring answers ever on this site. It would be good if you would label your axes - setting an example and all that.
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FlorisFeb 14 at 19:05

Why isn't the temperature of the water at 0 minutes 212 F?
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pentaneFeb 19 at 20:03

Was the "stirring" the sort that results in swirling, or top-bottom circulation, or what? Also, repeated measurement of each method would have given a sense of the noise in your measurement. Nice!
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BBrownFeb 28 at 22:42

As Georg correctly remarks, the latent heat of vaporization of water is enormous - but he's wrong about waving the spoon; stirring is the champion here.

Why? Temperature is really the average kinetic energy of the molecules in the bulk substance, which actually have a variety of individual kinetic energies. Stirring is the fastest way to bring high-kinetic-energy outlier water molecules to the surface, where they will overcome the electrostatic bonding mechanisms that keep them in the liquid phase, and jump into the air (vapor phase). This rapid decrease in the high-energy outliers is the quickest way to cool a hot aqueous solution.

It's similar to stirring iced tea. If you just plop ice cubes into a glass of warm tea, it will take quite a while for the warmer tea to cool; if you stir it vigorously, it will reach a cold equilibrium within seconds; the latent heat of fusion absorbed by the ice melting is similarly enormous.

This kind of thing has a lot of applications to laboratory and industrial chemical processes, surface catalysis, petroleum cracking, yadda yadda. You learn a lot about it in third-year university physical chemistry, and really must master it before or during graduate work as a chemist.

If you want an even faster way to cool a cup of coffee, here's a tip from my Granddad Parker: forget the spoon and saucer your coffee. In other words, pour the top part of it from the cup into a saucer, and then back again a few times. The large and constantly changing surface area during this process will cause extremely rapid evaporation of those high-energy outliers, much faster than stirring. Saucering was very common up through the Great Depression, which is one of the reasons older coffee sets always included saucers. You also get deep-ish saucers at many restaurants as a holdover from this practice, although I doubt many people do it any more.

""Use the spoon to add a spoonful of liquid helium to the coffee. Slowly."" Funny, this is the most ineffective and the most expensive method. :=)
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GeorgFeb 16 '11 at 18:49

2

@Chipaca--life's not fair:) you get +1 for basically stealing a variant of my answer and I get a -1 for a more subtle answer :) I am sure I could come up with a very large list of equally valuable answers...
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Gordon Feb 16 '11 at 18:55

2

@Gordon all lists of answers that are not the ones you wanted automatically tie in to the joke about the $FAMOUS_PHYSICIST who answered how to measure the hight of the building using a barometer... whereas just a single not-the-answer-you-wanted makes it look like you didn't understand the question.
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ChipacaFeb 16 '11 at 18:59

@Chipaca --nah, the list is just too much of a good thing--gilding the lily. Besides, how do you measure the "hight"?
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Gordon Feb 16 '11 at 21:00

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don't forget you'd need to be in an intensely-insulated room to "pour" liquid helium: it won't stay liquid in a normal atmosphere.. liquid nitrogen, on the other hand, will stay liquid in a normal atmosphere for a while - much better thermal inertia
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warrenFeb 17 '11 at 13:01

With respect to the content in the cup, all Your hampering
with the spoon is irrelevant. Cooling of a hot coffee is
achieved by vaporisation of water. At temperatures between
100 and say 50 °C the vapor pressure is so big, that the heat
carried away by convection of the hot (and much less dense
than air!) vapor dominates all other heat transfer mechanisms.
(ca 540 cal/g heat of vaporisation!)

So, because You do not "allow/accept" blowing the surface of the coffee,
the second best is to wave the spoon over the surface .
Blowing/waving will enhance the vaporisation due to quick replacement
of the vapour on top of the surface with fresh, cool, dry air.

Could stirring enhance vaporization in a similar way to your proposed spoon waving?
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Jaime SotoFeb 16 '11 at 15:47

3

@Jaime, Normally the decisive part of resistance to heat transfer is on the gaseouse side of the barrier. But in doubt, lets compromise, the spoon held a little bit deeper when waving will scratch the suface of the coffee and create some convection there too. :=)
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GeorgFeb 16 '11 at 15:59

I can't believe the density or material of the spoon hasn't been considered. If the spoon is very dense you can take it and wave it in the air in a 15° arc and say, "Dear waiter, if you don't put some cold milk in my coffee I will hit you between the eyes with this abnormally dense spoon".

On the other hand, if its made of gold or silver you hold it horizontal to the ground in a north south direction such that it refracts the light and say, "Dear waiter, here I have a brilliant and valuable spoon which I will give you in exchange for placing my coffee cup in a bath of ice til it cools"

Are you saying a 98% full cup of coffee cools off faster than a 70% full cup? Because the air is changing less with the coffee lower in the cup?
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corsiKaFeb 16 '11 at 17:48

3

@glowcoder If the cups are the same size, the fuller one has more coffee, so it will cool more slowly. There's just more heat mass to it. But if the 98% full cup is also thinner radially, so that it has the same amount of coffee, but the coffee is just closer to the rim, then yes: the moving air will cool it more quickly.
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spencer nelsonFeb 16 '11 at 20:52

@spencer Thank you for the clear explanation of something that isn't intuitive. (Well, maybe it's intuitive to you... I know just enough physics to make people think I know physics :D)
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corsiKaFeb 17 '11 at 8:07

pour a bit of coffee in the saucer ... and while you're at it, why don't you lap it, just like a kitty. The column of coffee between your tongue and the saucer will add to the surface even more.
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Alois MahdalNov 19 '13 at 1:47

This is the correct answer. I think evaporative cooling will exceed loss by conduction and radiation. The rate of evaporative heat loss depends on the surface area and the difference between (the partial pressure of water at the temperature describing the gas at the boundary) and the humidity of the air. Dipping the spoon and blowing on it would win, I would think. The spoonful of liquid stays warm long enough for taking your time about dipping, drawing down the spoon's heat without lowering its temperature much. If the spoon handle dries out, dip again!
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BBrownFeb 28 at 22:57

The answer may depend slightly on the humidity in the room (as that will determine the evaporative cooling rate), but basically your best bet is to increase the surface area of your coffee as much as possible and increase the rate of airflow over the coffee as much as possible (so that the local gradient of partial pressure of water vapor is as steep as possible). I suspect that your best bet would be to pick up spoonfuls of coffee and pour them back into the cup from as high as you can manage without splattering the coffee all over the place--the stream of falling liquid has a high surface to volume ratio and is traveling quickly.

The fastest and coolest way to cool the coffee, with only a cup and spoon, that is also theoretically possible, is to throw all the coffee up in the air, and with somewhat well-coordinated movement catch it all in the cup as it falls down. This maximises the total surface area of the coffee with the air per time, and thus also the total heat transfer.

Pre-cool the spoon first (in the freezer, or in your kitchen thermos of liquid nitrogen :) and put it in the cup. Periodically repeat the process with new spoons. Use a silver spoon (some of us were born with one in our mouths.)

Note: If you allow someone to take the spoon in and out of the coffee, the question allows much too much freedom of action--there is nothing in the bounds of the question to rule out cooling the spoon either then---hence, my answer, which was meant ironically, not seriously, for those who have trouble determining the difference...

@fortran --no one said no cheating ;) But in the rules you say that any other creative methods are welcome, so why the -1? The answer is a joke. I thought I could afford the knock on the rep points.
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Gordon Feb 16 '11 at 18:23

The fastest method for cooling coffee (or hot chocolate, as I'm more likely to drink) I've discovered when I don't have a saucer or second cup is to ignore the spoon altogether.

Without a saucer, spoon, or blowing, I first place my hands around the container without any insulation device and let my hands absorb as much heat as they can stand. I then move my hands to the table to transfer the heat to the table. I then repeat the cupping the cup and transferring to the table as necessary. Within 1-2 minutes I can take a 200+ degree cup down to pleasantly drinkable levels.

This method is all about conducting the heat out of the container to the environment, and has the convenient secondary benefit of warming your hands (and the rest of your body) very quickly while waiting for your drink to cool. Combine it with a swishing of the cup to bring down the overall temperature of the coffee (not just the sides), as well as blowing on the surface (if you are allowed to cheat), and the cup cools even faster.

This works best with glass or metal tables, but wood tables also work well.

The organization of the surface of water is an impediment to the diffusion of gases. For example, an unstirred (~5 ml) oximeter cell will take about 10 minutes to equilibrate with atmospheric oxygen, while a stirred cell will equilibrate in under a minute.

Surface foam, or a monolayer of fatty molecules, such as might be formed by coffee oils or creamer, likely has insulative value. Stirring would minimize that by disrupting the structure.

I would say use the room temperature, lift the coffee with the soon and drop it back to the cup repeatedly, this will make a part of the coffee be in contact with the cold room hence getting colder and mixing with the hot one bringing down the overall temperature.

I have (obviously??) no mathematical / physical knowledge about how effective this technique might be, and besides I drink the coffee as hot as I can ;P

Stir the coffee with the spoon and blow air into the cup with your mouth. Every few seconds change the direction of the stir (clockwise to counterclockwise and vice-versa). This should cool it quickly than just stirring the coffee with the spoon.

By leaving the spoon stationary in the coffee, you are only benefiting from the thermal conduction and dissipation of the spoon.

By stirring the coffee, you are not only helping to keep the hottest parts of the coffee in contact with the air & cup, increasing the surface area by introducing abnormalities in the top surface, and helping to move the warm, moist air atop the coffee, but you are also getting all of the benefits of the thermal conduction and dissipation of the spoon.

By dunking the spoon repeatedly, you are not only introducing air into the liquid, which will grab lots of heat and be whisked away as soon as it hits the surface, but you are also getting all of the benefits of the thermal conduction and dissipation of the spoon and all of the benefits of stirring the coffee.

Ignoring the fact that you will probably splash the coffee and make a mess of the counter, the correct answer is repeatedly dunking the spoon. Also, you and your coworkers are nerds!

I stir the coffee in a side to side motion with the spoon bowl parallel to the side of the cup. Due to the angle bernoulli's principle moves the coffee through the center of the cup towards the top. This circulates the liquid much more quickly than you'd expect in a controllable fashion that avoids splashing vigorous stirring can cause. It also has the side effect of removing the dry creamer from the bowl of the spoon far more efficiently than any other possible motion. The liquid coming up from the center and being forced across the top to the sides smoothly and without cavitation gaps stirring causes. The liquid also conducts with the sides better and releases heat both via the wave that forms at the top increasing the surface area contact with air and transferring the heat to the body of the cup/heat radiator.
Actually I do stir that way. It cleans the spoon far better and requires less effort. Other than that the above is merely serendipitous inference.

Use the tongue and palate to cool spoon pushing hard. When the spoon is close to the temperature of your mouth (feels tepid) remove it and reinsert the spoon in the coffee by another 3 secondos plus 0.5 multiplied by the times you have inserted the spoon.